I. Introduction
Physical-layer network coding (PNC), originally proposed in [1], [2], can significantly boost the throughput of multi-user wireless communication networks. Generally, PNC transmissions in a relay network consist of two phases: multiple access phase and broadcast phase. In the multiple access phase, multiple source nodes transmit signals to a relay simultaneously. The relay aims to decode the overlapped signals into network coded (NC) messages. One basic setup for PNC is a wireless two-way relay channel (TWRC), in which two users exchange information from each other via an intermediate relay. The simplest form for the target NC messages is the bit-wise exclusive-or (XOR) of the two source messages [1]–[5].